Jan de Leeuw <[EMAIL PROTECTED]> wrote:
> This is one of the areas in which we cannot be precise enough. An
> observed statistics is not a random variable, but
> a realization of a random variable. Random variables
> are theoretical or mathematical constructs, which are never observed
> directly. In frequentist statistics the random variable corresponds with the
> framework of (hypothetical) replications, in Bayesian statistics
> with the (equally hypothetical) subjective beliefs.
> Thus observed statistics do not have sampling distributions, the
> corresponding random variables (of which we assume the statistics
> are realizations) have sampling distributions, where the "sampling"
> usually refers to a theoretical framework of repeated independent
> trials.
> As for log(ad/bc), any differentiable function of the observed
> proportions is asymptotically normal. Of course, given the above,
> this really should state that any differentiable function of the
> random variables of which the observed proportions are supposedly
> realizations is asymptotically normal (if suitably normalized).
> Statistics is useful because it provides a hypothetical framework
> of replications, and thus it often is most useful in areas in which
> actual replications are impossible or very expensive.
Of *course* I meant to say that the observed "ad/bc" was a value
of a random variable and not a random variable itself.
I was responding to Mr. Ullrich's implication that while,
on the one hand the observed "chi-squared" value can be interpreted as
a test statistic, on the other hand, the observed "odds ratio" is
not a test statistic but a measure of effect size.
I was simply pointing out that any combination of a,b,c,d
can be, in principle, be used as a "test statistic", since,
in principle, one could cook up an approximate sampling
distribution for any "reasonable" combination of a,b,c,d. There is
nothing about the odds ratio that makes intrinsically
less suitable for being treated as an *instance* of
a random variable, than -- say -- the chi-squared statistic.
So I stand corrected for a semantic gaffe, but the point
I was trying to make in the discussion is no less worth
a response on that account alone.
Ron
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